Path Reweighting Methods for underdamped Langevin Dynamics for Molecular Systems

Abstract

Knowledge about the dynamical properties of biomolecules is essential to understand their function in biological processes. This thesis approaches the task to compute dynamical properties with two different strategies. Part A focuses on Molecular Dynamics (MD) simulations combined with path reweighting. Three of the most widely used underdamped Langevin integrators for MD simulations are the splitting methods BAOAB and BAOA which are available in the MD packages OpenMM and AMBER and the Gromacs Stochastic Dynamics (GSD) integrator implemented in GROMACS. We found that all three integrators are equivalent configurational sampling algorithms and thus yield configurational properties at equivalent accuracy. MD simulations with stochastic integrators such as Langevin integrators offer the possibility to reweight estimated dynamical properties using path reweighting. With path reweighting we can for example recover the original dynamics from MD simulation that have been conducted with enhanced sampling methods. The key component of path reweighting is the path reweighting factor M which strongly depends on the chosen integrator. We derive M_L for underdamped Langevin dynamics propagated by a variant of the Langevin Leapfrog integrator. Additionally, we present two strategies which can be used as blueprints to straightforwardly derive M_L for other Langevin integrators. The previously reported path reweighting factor matches the Euler-Maruyama integrator for overdamped Langevin dynamics and was used as standard reweighting factor even though the MD simulation was conducted with an underdamped Langevin integrator. We prove that this path reweighting factors differs from the exact M_L only by O(ξ^4 ∆t^4) and thus yields highly accurate dynamical reweighting results (∆t is the integration time step, and ξ is the collision rate.). Part B of this thesis combines experimental and theoretical approaches to investigate Multiple Inositol Polyphosphate Phosphatase 1 (MINPP1)-mediated inositol polyphosphate (InsP) networks. We use 13C-labeling experiments combined with nuclear magnetic resonance spectroscopy (NMR) to uncover a novel branch of InsP dephosphorylation in human cells. Additionally, we extract the corresponding reaction rates using a Markovian kinetic scheme as theoretical model to describe the network.